What is _{i}ⁿ x_i f_i equal to ?

Correct Answer is : 2n+1−n−22n−1\;{2ⁿ+1}-n-2}{2ⁿ-1}}2n−12n+1−n−2

Correct Answer is : 2n+1−n−22n−1\;{2ⁿ+1}-n-2}{2ⁿ-1}}2n−12n+1−n−2

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UPSC NDA I 2024 Mathematics Paper

Consider the following for the next two (02) items that follow :

$x_i$	1	2	3	$⋯$	$n$
$f_i$	1	$2^{-1}$	$2^{-2}$	$. . .$	$2^{-(n-1)}$

Question : 117 of 120

Marks: +1, -0

What is

\sum\limits_{i}^{n} x_i f_i

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